Modeling of Power Distribution Networks for Path Finding

Abstract

In a method for analyzing pre-register-transfer level phase of a power distribution network in an electronic circuit design, in which the power distribution network is defined to include a matrix of a number repeated leaf cells, wherein each of the matrix of repeated leaf cells corresponds to a model leaf cell wherein the model leaf cell includes an alternating Vdd and Gnd grid on top of an interposer. A plurality of local ports of the model leaf cell is defined. The plurality of local ports is defined where each of the matrix of repeated leaf cells is coupled to adjacent ones of the matrix of repeated leaf cells. The model leaf cell is simulated using an implementation of an integral equation based solver to compute electromagnetic scattering parameters (S-parameters) that correspond to the model leaf cell. The electromagnetic S-parameters are cascaded across the matrix using a binary merge algorithm. S-parameters of any non-periodic power distribution network component models are coupled to the S-parameters of the matrix. An overall impedance response of the power distribution network is computed based on S-parameters of the matrix and the S-parameters of any non-periodic power distribution network component models using an integrated circuit modelling program.

What is claimed is: 
     
         1 . A method for analyzing pre-register-transfer level phase of a power distribution network in an electronic circuit design, comprising the steps of:
 (a) defining the power distribution network to include a matrix of a number repeated leaf cells, wherein each of the matrix of repeated leaf cells corresponds to a model leaf cell wherein the model leaf cell includes an alternating Vdd and Gnd grid on top of an interposer;   (b) defining a plurality of local ports of the model leaf cell, the plurality of local ports being defined where each of the matrix of repeated leaf cells is coupled to adjacent ones of the matrix of repeated leaf cells;   (c) simulating the model leaf cell using an implementation of an integral equation based solver to compute electromagnetic scattering parameters (S-parameters) that correspond to the model leaf cell;   (d) cascading the electromagnetic S-parameters across the matrix using a binary merge algorithm;   (e) coupling S-parameters of any non-periodic power distribution network component models to the S-parameters of the matrix; and   (f) computing an overall impedance response of the power distribution network based on S-parameters of the matrix and the S-parameters of any non-periodic power distribution network component models using an integrated circuit modelling program.   
     
     
         2 . The method of  claim 1 , wherein the interposer comprises a selected one of a silicon interposer, an organic interposer and a ceramic packaging interposer. 
     
     
         3 . The method of  claim 1 , wherein the local ports are defined along peripheral edges of the leaf cell. 
     
     
         4 . The method of  claim 1 , further comprising the steps of:
 (a) defining the leaf cell to include at least one power via or at least one through silicon via (TSV) to provide a Vdd power coupling to the grid; and   (b) defining the leaf cell to include at least one Gnd via or at least one TSV to provide a Gnd coupling to the grid.   
     
     
         5 . The method of  claim 1 , wherein the binary merge algorithm includes the steps of:
 (a) generating a binary number that corresponds to the number of leaf cells in the matrix;   (b) merging the S-parameters of two adjacent leaf cells to generate a primary higher order lateral structure;   (c) merging S-parameters of two first higher order lateral structures to generate a secondary higher order lateral structure;   (d) continuing to merge higher order lateral structures to generate successively higher order lateral structures until all of the S-parameters of each leaf cell in a row of the matrix of leaf cells are merged;   (e) merging S-parameters of each row of leaf cells into successive higher order vertical structures until the S-parameters of all leaf cells in the matrix are merged.   
     
     
         6 . The method of  claim 1 , wherein the alternating Vdd and Gnd grid comprises at least one Vdd conductor and at least one Gnd conductor disposed on a first plane. 
     
     
         7 . The method of  claim 6 , wherein the alternating Vdd and Gnd grid further comprises:
 (a) at least one Vdd conductor and at least one Gnd conductor disposed on a second plane; and   (b) a dielectric disposed between the first plane and the second plane.   
     
     
         8 . The method of  claim 7 , wherein the model leaf cell further comprises:
 (a) a first via that couples the Vdd conductor on the first plane to the Vdd conductor on the second plane; and   (b) a second via that couples the Gnd conductor on the first plane to the Gnd conductor on the second plane.   
     
     
         9 . A circuit simulation method for analyzing pre-register-transfer level phase of a power distribution network in an electronic circuit design, comprising the steps of:
 (a) defining the power distribution network to include a matrix of repeated leaf cells, wherein each of the matrix of repeated leaf cells corresponds to a model leaf cell wherein the model leaf cell includes an alternating Vdd and Gnd grid on top of a silicon interposer;   (b) defining the model leaf cell to include at least one power through silicon via (TSV) to provide a Vdd power coupling to the grid;   (c) defining the model leaf cell to include at least one Gnd TSV to provide a Gnd coupling to the grid;   (d) defining a plurality of local ports along peripheral edges of the model leaf cell, the plurality of local ports being defined where each of the matrix of repeated leaf cells is coupled to adjacent ones of the matrix of repeated leaf cells;   (e) simulating the model leaf cell using an implementation of an integral equation based solver to compute electromagnetic scattering parameters (S-parameters) that correspond to the model leaf cell;   (f) cascading the electromagnetic S-parameters across the matrix using a binary merge algorithm, wherein the binary merge algorithm includes the steps of:
 (i) merging the S-parameters of two adjacent leaf cells to generate a primary higher order lateral structure; 
 (ii) merging S-parameters of two first higher order lateral structures to generate a secondary higher order lateral structure; 
 (iii) continuing to merge higher order lateral structures to generate successively higher order lateral structures until all of the S-parameters of each leaf cell in a row of the matrix of leaf cells are merged; and 
 (iv) merging S-parameters of each row of leaf cells into successive higher order vertical structures until the S-parameters of all leaf cells in the matrix are merged; 
   (g) coupling S-parameters of any non-periodic power distribution network component models to the S-parameters of the matrix; and   (h) computing an overall impedance response of the power distribution network based on S-parameters of the matrix and the S-parameters of any non-periodic power distribution network component models using an integrated circuit modelling program.   
     
     
         10 . The circuit simulation method of  claim 9 , further comprising the steps of:
 (a) defining the leaf cell to include at least one power through silicon via (TSV) to provide a Vdd power coupling to the grid; and   (b) defining the leaf cell to include at least one Gnd TSV to provide a Gnd coupling to the grid.   
     
     
         11 . The circuit simulation method of  claim 9 , wherein the alternating Vdd and Gnd grid comprises at least one Vdd conductor and at least one Gnd conductor disposed on a first plane. 
     
     
         12 . The circuit simulation method of  claim 11 , wherein the alternating Vdd and Gnd grid further comprises:
 (a) at least one Vdd conductor and at least one Gnd conductor disposed on a second plane; and   (b) a dielectric disposed between the first plane and the second plane.   
     
     
         13 . The circuit simulation method of  claim 12 , wherein the model leaf cell further comprises:
 (a) a first via that couples the Vdd conductor on the first plane to the Vdd conductor on the second plane; and   (b) a second via that couples the Gnd conductor on the first plane to the Gnd conductor on the second plane.